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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.20424 |
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| _version_ | 1866915878140903424 |
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| author | Haulmark, Matthew Manning, Jason Fox |
| author_facet | Haulmark, Matthew Manning, Jason Fox |
| contents | In this paper, we obtain an action on a cube complex from an action on a path-connected topological space with a system of divisions. In the settings of hyperbolic groups or relatively hyperbolic groups with no peripheral splittings, our result provides an alternate route to Sageev's construction of a cube complex action from a collection of (relatively) quasiconvex subgroups of a (relatively) hyperbolic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20424 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From cut sets to cube complexes Haulmark, Matthew Manning, Jason Fox Group Theory 20F65, 20F67 In this paper, we obtain an action on a cube complex from an action on a path-connected topological space with a system of divisions. In the settings of hyperbolic groups or relatively hyperbolic groups with no peripheral splittings, our result provides an alternate route to Sageev's construction of a cube complex action from a collection of (relatively) quasiconvex subgroups of a (relatively) hyperbolic group. |
| title | From cut sets to cube complexes |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2603.20424 |